U.S. patent number 9,812,779 [Application Number 15/010,165] was granted by the patent office on 2017-11-07 for modulation patterns for surface scattering antennas.
This patent grant is currently assigned to The Invention Science Fund I LLC. The grantee listed for this patent is Searete LLC. Invention is credited to Pai-Yen Chen, Tom Driscoll, Siamak Ebadi, John Desmond Hunt, Nathan Ingle Landy, Melroy Machado, Milton Perque, Jr., David R. Smith, Yaroslav A. Urzhumov.
United States Patent |
9,812,779 |
Chen , et al. |
November 7, 2017 |
Modulation patterns for surface scattering antennas
Abstract
Modulation patterns for surface scattering antennas provide
desired antenna pattern attributes such as reduced side lobes and
reduced grating lobes.
Inventors: |
Chen; Pai-Yen (Houston, TX),
Driscoll; Tom (San Diego, CA), Ebadi; Siamak (Redmond,
WA), Hunt; John Desmond (Seattle, WA), Landy; Nathan
Ingle (Mercer Island, WA), Machado; Melroy (Seattle,
WA), Perque, Jr.; Milton (Seattle, WA), Smith; David
R. (Durham, NC), Urzhumov; Yaroslav A. (Bellevue,
WA) |
Applicant: |
Name |
City |
State |
Country |
Type |
Searete LLC |
Bellevue |
WA |
US |
|
|
Assignee: |
The Invention Science Fund I
LLC (N/A)
|
Family
ID: |
54870489 |
Appl.
No.: |
15/010,165 |
Filed: |
January 29, 2016 |
Prior Publication Data
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Document
Identifier |
Publication Date |
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US 20160149310 A1 |
May 26, 2016 |
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Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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14549928 |
Nov 21, 2014 |
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14510947 |
Oct 9, 2014 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
H01Q
11/02 (20130101); H01Q 3/44 (20130101); H01Q
13/20 (20130101) |
Current International
Class: |
H01Q
11/02 (20060101); H01Q 3/44 (20060101); H01Q
13/20 (20060101) |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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2007-081825 |
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Mar 2007 |
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JP |
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2008-054146 |
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Mar 2008 |
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JP |
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2010-187141 |
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Aug 2010 |
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JP |
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10-1045585 |
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Jun 2011 |
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KR |
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WO 2008-007545 |
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Jan 2008 |
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WO |
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WO 2008/059292 |
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May 2008 |
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WO |
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WO 2009/103042 |
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Aug 2009 |
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WO |
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WO 2010/021736 |
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Feb 2010 |
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WO |
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PCT/US2013/212504 |
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May 2013 |
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WO |
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WO 2013/147470 |
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Oct 2013 |
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WO |
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|
Primary Examiner: Han; Jessica
Assistant Examiner: Bouizza; Michael
Parent Case Text
CROSS-REFERENCE TO RELATED APPLICATIONS
The present application is related to and/or claims the benefit of
the earliest available effective filing date(s) from the following
listed application(s) (the "Priority Applications"), if any, listed
below (e.g., claims earliest available priority dates for other
than provisional patent applications or claims benefits under 35
USC .sctn.119(e) for provisional patent applications, for any and
all parent, grandparent, great-grandparent, etc. applications of
the Priority Application(s)). In addition, the present application
is related to the "Related Applications," if any, listed below.
PRIORITY APPLICATIONS
The present application constitutes a continuation-in-part of U.S.
patent application Ser. No. 14/510,947, entitled MODULATION
PATTERNS FOR SURFACE SCATTERING ANTENNAS, naming Pai-Yen Chen, Tom
Driscoll, Siamak Ebadi, John Desmond Hunt, Nathan Ingle Landy,
Melroy Machado, Milton Perque, Jr., David R. Smith, and Yaroslav A.
Urzhumov as inventors, filed 9, Oct., 2014, which is currently
co-pending or is an application of which a currently co-pending
application is entitled to the benefit of the filing date.
The present application constitutes a continuation-in-part of U.S.
patent application Ser. No. 14/549,928, entitled MODULATION
PATTERNS FOR SURFACE SCATTERING ANTENNAS, naming Pai-Yen Chen, Tom
Driscoll, Siamak Ebadi, John Desmond Hunt, Nathan Ingle Landy,
Melroy Machado, Milton Perque, Jr., David R. Smith, and Yaroslav A.
Urzhumov as inventors, filed 21, Nov., 2014, which is currently
co-pending or is an application of which a currently co-pending
application is entitled to the benefit of the filing date.
U.S. Patent Application No. 61/455,171, entitled SURFACE SCATTERING
ANTENNAS, naming NATHAN KUNDTZ ET AL. as inventors, filed Oct. 15,
2010, is related to the present application.
U.S. patent application Ser. No. 13/317,338, entitled SURFACE
SCATTERING ANTENNAS, naming ADAM BILY, ANNA K. BOARDMAN, RUSSELL J.
HANNIGAN, JOHN HUNT, NATHAN KUNDTZ, DAVID R. NASH, RYAN ALLAN
STEVENSON, AND PHILIP A. SULLIVAN as inventors, filed Oct. 14,
2011, is related to the present application.
U.S. patent application Ser. No. 13/838,934, entitled SURFACE
SCATTERING ANTENNA IMPROVEMENTS, naming ADAM BILY, JEFF DALLAS,
RUSSELL J. HANNIGAN, NATHAN KUNDTZ, DAVID R. NASH, AND RYAN ALLAN
STEVEN as inventors, filed Mar. 15, 2013, is related to the present
application.
U.S. Patent Application No. 61/988,023, entitled SURFACE SCATTERING
ANTENNAS WITH LUMPED ELEMENTS, naming PAI-YEN CHEN, TOM DRISCOLL,
SIAMAK EBADI, JOHN DESMOND HUNT, NATHAN INGLE LANDY, MELROY
MACHADO, MILTON PERQUE, DAVID R. SMITH, AND YAROSLAV A. URZHUMOV as
inventors, filed May 2, 2014, is related to the present
application.
U.S. patent application Ser. No. 14/506,432, entitled SURFACE
SCATTERING ANTENNAS WITH LUMPED ELEMENTS, naming PAI-YEN CHEN, TOM
DRISCOLL, SIAMAK EBADI, JOHN DESMOND HUNT, NATHAN INGLE LANDY,
MELROY MACHADO, JAY MCCANDLESS, MILTON PERQUE, DAVID R. SMITH, AND
YAROSLAV A. URZHUMOV as inventors, filed Oct. 3, 2014, is related
to the present application.
U.S. Patent Application No. 61/992,699, entitled CURVED SURFACE
SCATTERING ANTENNAS, naming PAI-YEN CHEN, TOM DRISCOLL, SIAMAK
EBADI, JOHN DESMOND HUNT, NATHAN INGLE LANDY, MELROY MACHADO,
MILTON PERQUE, DAVID R. SMITH, AND YAROSLAV A. URZHUMOV as
inventors, filed May 13, 2014, is related to the present
application.
The present application claims benefit of priority of U.S.
Provisional Patent Application No. 62/015,293, entitled MODULATION
PATTERNS FOR SURFACE SCATTERING ANTENNAS, naming PAI-YEN CHEN, TOM
DRISCOLL, SIAMAK EBADI, JOHN DESMOND HUNT, NATHAN INGLE LANDY,
MELROY MACHADO, MILTON PERQUE, DAVID R. SMITH, AND YAROSLAV A.
URZHUMOV as inventors, filed Jun. 20, 2014, which was filed within
the twelve months preceding the filing date of the present
application.
All subject matter of all of the above applications is incorporated
herein by reference to the extent such subject matter is not
inconsistent herewith.
Claims
What is claimed is:
1. A method, comprising: discretizing a hologram function for a
surface scattering antenna that defines an aperture, where the
discretizing includes identifying a discrete plurality of locations
on the aperture for a discrete plurality of scattering elements of
the surface scattering antenna and identifying a discrete set of
states for each of the scattering elements corresponding to a
discrete set of function values at each of the locations of the
scattering elements; and identifying an antenna configuration that
reduces artifacts attributable to the discretizing, wherein the
identifying of the antenna configuration includes altering a
Fourier spectrum of the discretized hologram function.
2. The method of claim 1, further comprising: adjusting the surface
scattering antenna to the identified antenna configuration.
3. The method of claim 1, further comprising: operating the surface
scattering antenna in the identified antenna configuration.
4. The method of claim 1, further comprising: storing the
identified antenna configuration in a storage medium.
5. The method of claim 1, wherein the altering of the Fourier
spectrum of the discretized hologram function includes, for each
location in the plurality of scattering locations: identifying a
first contribution of the location to one or more desired spatial
Fourier components of the discretized hologram function;
identifying a second contribution of the location to one or more
undesired spatial Fourier components of the discretized hologram
function; and selecting a function value for the location from the
discrete set of functions values, where the selected value equals:
a value in the discrete set of function values that is closest to
the hologram function evaluated at the location, if the ratio of
the first contribution to the second contribution is greater than a
selected amount; or a minimum value in the discrete set of function
value, if the ratio of the first contribution to the second
contribution is less than or equal to a selected amount.
6. The method of claim 5, wherein the one or more desired spatial
Fourier components are fundamental spatial Fourier components of
the discretized hologram function.
7. The method of claim 5, wherein the one or more undesired spatial
Fourier components include a harmonic spatial Fourier component of
the discretized hologram at a non-evanescent spatial frequency.
8. The method of claim 5, wherein the one or more undesired spatial
Fourier components include a harmonic spatial Fourier component of
the discretized hologram at a evanescent spatial frequency that is
aliased to a non-evanescent spatial frequency by the discretizing
of the discrete plurality of locations.
9. The method of claim 5, wherein the identifying of the antenna
configuration includes, for each scattering element in the
plurality of scattering elements: identifying a state for the
scattering element selected from the discrete set of states and
corresponding to the selected function value for the location of
the scattering element.
10. The method of claim 1, wherein the altering of the Fourier
spectrum of the discretized hologram function includes: altering
the hologram function by replacing a fundamental spatial Fourier
component of the hologram function with a plurality of spatial
Fourier components.
11. The method of claim 10, wherein the plurality of spatial
Fourier components is a discrete set of Fourier components within a
selected spatial frequency bandwidth around a fundamental spatial
frequency corresponding to the fundamental spatial Fourier
component.
12. The method of claim 10, wherein the plurality of spatial
Fourier components is a continuous spectrum of Fourier components
within a selected spatial frequency bandwidth around a fundamental
spatial frequency corresponding to the fundamental spatial Fourier
component.
13. The method of claim 1, wherein the altering of the Fourier
spectrum of the discretized hologram function includes: altering
the discretized hologram function by selectively reducing a
harmonic spatial Fourier component of the discretized hologram
function.
14. The method of claim 13, wherein the selectively reducing
includes selectively eliminating the harmonic spatial Fourier
component.
15. The method of claim 13, wherein the selectively-reduced
harmonic spatial Fourier component is a harmonic spatial Fourier
component at a non-evanescent spatial frequency.
16. The method of claim 13, wherein the selectively-reduced
harmonic spatial Fourier component is a harmonic spatial Fourier
component at a evanescent spatial frequency that is aliased to a
non-evanescent spatial frequency by the discretizing of the
discrete plurality of locations.
17. A system, comprising: a surface scattering antenna with a
plurality of adjustable scattering elements that are adjustable
between a discrete set of states corresponding to a discrete set of
function values at each location in a plurality of locations for
the plurality of adjustable scattering elements; a storage medium
on which a set of antenna configurations corresponding to a set of
hologram functions is written, each antenna configuration being
selected to reduce artifacts attributable to a discretization of
the respective hologram function; and control circuitry operable to
read antenna configurations from the storage medium and adjust the
plurality of adjustable scattering elements to provide the antenna
configurations; wherein at least one antenna configuration is a
Fourier-spectrum-altered discretization of the respective hologram
function.
18. The system of claim 17, wherein the adjustable scattering
elements are adjustable between a discrete set of states including
a minimum state, and the Fourier-spectrum-altered discretization of
the respective hologram function includes one or more scattering
elements set to the minimum state to reduce their disproportional
contribution to one or more undesired spatial Fourier components of
the discretization of the respective hologram function.
19. The system of claim 18, wherein the one or more undesired
spatial Fourier components include a harmonic spatial Fourier
component of the discretization at a non-evanescent spatial
frequency.
20. The system of claim 18, wherein the one or more undesired
spatial Fourier components include a harmonic spatial Fourier
component of the discretization at an evanescent spatial frequency
that is aliased to a non-evanescent spatial frequency by the
discretization.
21. The system of claim 17, wherein the Fourier-spectrum-altered
discretization of the respective hologram function is a
discretization of an altered hologram function that replaces a
fundamental spatial Fourier component of the respective hologram
function with a plurality of spatial Fourier components.
22. The system of claim 21, wherein the plurality of spatial
Fourier components is a discrete set of Fourier components within a
selected spatial frequency bandwidth around a fundamental spatial
frequency corresponding to the fundamental spatial Fourier
component.
23. The system of claim 21, wherein the plurality of spatial
Fourier components is a continuous spectrum of Fourier components
within a selected spatial frequency bandwidth around a fundamental
spatial frequency corresponding to the fundamental spatial Fourier
component.
24. The system of claim 17, wherein the Fourier-spectrum-altered
discretization of the respective hologram function is an altered
discretization of the respective hologram function that selectively
reduces a harmonic spatial Fourier components of the discretization
of the respective hologram function.
25. The system of claim 24, wherein the altered discretization that
selectively reduces the harmonic spatial Fourier components is an
altered discretization that selectively eliminates the harmonic
spatial Fourier component.
26. The system of claim 24, wherein the selectively-reduced
harmonic spatial Fourier component is a harmonic spatial Fourier
component at a non-evanescent spatial frequency.
27. The system of claim 24, wherein the selectively-reduced
harmonic spatial Fourier component is a harmonic spatial Fourier
component at a evanescent spatial frequency that is aliased to a
non-evanescent spatial frequency by the discretization.
28. A method of controlling a surface scattering antenna with a
plurality of adjustable scattering elements, comprising: reading an
antenna configuration from a storage medium, the antenna
configuration being selected to reduce artifacts attributable to a
discretization of a hologram function; and adjusting the plurality
of adjustable scattering elements to provide the antenna
configuration; wherein the adjustable scattering elements are
adjustable between a discrete set of states corresponding to a
discrete set of function values at each location in a plurality of
locations for the plurality of adjustable scattering elements; and
wherein the antenna configuration is a Fourier-spectrum-altered
discretization of the hologram function.
29. The method of claim 28, further comprising: operating the
antenna in the antenna configuration.
30. The method of claim 28, wherein the adjustable scattering
elements are adjustable between a discrete set of states including
a minimum state, and the antenna configuration includes one or more
scattering elements set to the minimum state to reduce their
disproportional contribution to one or more undesired spatial
Fourier components of the discretization of the hologram
function.
31. The method of claim 30, wherein the one or more undesired
spatial Fourier components include a harmonic spatial Fourier
component of the discretization at a non-evanescent spatial
frequency.
32. The method of claim 30, wherein the one or more undesired
spatial Fourier components include a harmonic spatial Fourier
component of the discretization at an evanescent spatial frequency
that is aliased to a non-evanescent spatial frequency by the
discretization.
33. The method of claim 28, wherein the Fourier-spectrum-altered
discretization is a discretization of an altered hologram function
that replaces a fundamental spatial Fourier component of the
hologram function with a plurality of spatial Fourier
components.
34. The method of claim 33, wherein the plurality of spatial
Fourier components is a discrete set of Fourier components within a
selected spatial frequency bandwidth around a fundamental spatial
frequency corresponding to the fundamental spatial Fourier
component.
35. The method of claim 33, wherein the plurality of spatial
Fourier components is a continuous spectrum of Fourier components
within a selected spatial frequency bandwidth around a fundamental
spatial frequency corresponding to the fundamental spatial Fourier
component.
36. The method of claim 28, wherein the Fourier-spectrum-altered
discretization is an altered discretization of the hologram
function that selectively reduces a harmonic spatial Fourier
component of the discretization of the hologram function.
37. The method of claim 36, wherein the altered discretization that
selectively reduces the harmonic spatial Fourier components is an
altered discretization that selectively eliminates the harmonic
spatial Fourier component.
38. The method of claim 36, wherein the selectively-reduced
harmonic spatial Fourier component is a harmonic spatial Fourier
component at a non-evanescent spatial frequency.
39. The method of claim 36, wherein the selectively-reduced
harmonic spatial Fourier component is a harmonic spatial Fourier
component at a evanescent spatial frequency that is aliased to a
non-evanescent spatial frequency by the discretization.
Description
BRIEF DESCRIPTION OF THE FIGURES
FIG. 1 is a schematic depiction of a surface scattering
antenna.
FIGS. 2A and 2B respectively depict an exemplary adjustment pattern
and corresponding beam pattern for a surface scattering
antenna.
FIGS. 3A and 3B respectively depict another exemplary adjustment
pattern and corresponding beam pattern for a surface scattering
antenna.
FIGS. 4A and 4B respectively depict another exemplary adjustment
pattern and corresponding field pattern for a surface scattering
antenna.
FIGS. 5A-5F depict an example of hologram discretization and
aliasing.
FIG. 6 depicts a system block diagram.
DETAILED DESCRIPTION
In the following detailed description, reference is made to the
accompanying drawings, which form a part hereof. In the drawings,
similar symbols typically identify similar components, unless
context dictates otherwise. The illustrative embodiments described
in the detailed description, drawings, and claims are not meant to
be limiting. Other embodiments may be utilized, and other changes
may be made, without departing from the spirit or scope of the
subject matter presented here.
A schematic illustration of a surface scattering antenna is
depicted in FIG. 1. The surface scattering antenna 100 includes a
plurality of scattering elements 102a, 102b that are distributed
along a wave-propagating structure 104. The wave propagating
structure 104 may be a microstrip, a coplanar waveguide, a parallel
plate waveguide, a dielectric rod or slab, a closed or tubular
waveguide, a substrate-integrated waveguide, or any other structure
capable of supporting the propagation of a guided wave or surface
wave 105 along or within the structure. The wavy line 105 is a
symbolic depiction of the guided wave or surface wave, and this
symbolic depiction is not intended to indicate an actual wavelength
or amplitude of the guided wave or surface wave; moreover, while
the wavy line 105 is depicted as within the wave-propagating
structure 104 (e.g. as for a guided wave in a metallic waveguide),
for a surface wave the wave may be substantially localized outside
the wave-propagating structure (e.g. as for a TM mode on a single
wire transmission line or a "spoof plasmon" on an artificial
impedance surface). It is also to be noted that while the
disclosure herein generally refers to the guided wave or surface
wave 105 as a propagating wave, other embodiments are contemplated
that make use of a standing wave that is a superposition of an
input wave and reflection(s) thereof. The scattering elements 102a,
102b may include scattering elements that are embedded within,
positioned on a surface of, or positioned within an evanescent
proximity of, the wave-propagation structure 104. For example, the
scattering elements can include complementary metamaterial elements
such as those presented in D. R. Smith et al, "Metamaterials for
surfaces and waveguides," U.S. Patent Application Publication No.
2010/0156573, and A. Bily et al, "Surface scattering antennas,"
U.S. Patent Application Publication No. 2012/0194399, each of which
is herein incorporated by reference. As another example, the
scattering elements can include patch elements such as those
presented in A. Bily et al, "Surface scattering antenna
improvements," U.S. U.S. patent application Ser. No. 13/838,934,
which is herein incorporated by reference.
The surface scattering antenna also includes at least one feed
connector 106 that is configured to couple the wave-propagation
structure 104 to a feed structure 108. The feed structure 108
(schematically depicted as a coaxial cable) may be a transmission
line, a waveguide, or any other structure capable of providing an
electromagnetic signal that may be launched, via the feed connector
106, into a guided wave or surface wave 105 of the wave-propagating
structure 104. The feed connector 106 may be, for example, a
coaxial-to-microstrip connector (e.g. an SMA-to-PCB adapter), a
coaxial-to-waveguide connector, a mode-matched transition section,
etc. While FIG. 1 depicts the feed connector in an "end-launch"
configuration, whereby the guided wave or surface wave 105 may be
launched from a peripheral region of the wave-propagating structure
(e.g. from an end of a microstrip or from an edge of a parallel
plate waveguide), in other embodiments the feed structure may be
attached to a non-peripheral portion of the wave-propagating
structure, whereby the guided wave or surface wave 105 may be
launched from that non-peripheral portion of the wave-propagating
structure (e.g. from a midpoint of a microstrip or through a hole
drilled in a top or bottom plate of a parallel plate waveguide);
and yet other embodiments may provide a plurality of feed
connectors attached to the wave-propagating structure at a
plurality of locations (peripheral and/or non-peripheral).
The scattering elements 102a, 102b are adjustable scattering
elements having electromagnetic properties that are adjustable in
response to one or more external inputs. Various embodiments of
adjustable scattering elements are described, for example, in D. R.
Smith et al, previously cited, and further in this disclosure.
Adjustable scattering elements can include elements that are
adjustable in response to voltage inputs (e.g. bias voltages for
active elements (such as varactors, transistors, diodes) or for
elements that incorporate tunable dielectric materials (such as
ferroelectrics or liquid crystals)), current inputs (e.g. direct
injection of charge carriers into active elements), optical inputs
(e.g. illumination of a photoactive material), field inputs (e.g.
magnetic fields for elements that include nonlinear magnetic
materials), mechanical inputs (e.g. MEMS, actuators, hydraulics),
etc. In the schematic example of FIG. 1, scattering elements that
have been adjusted to a first state having first electromagnetic
properties are depicted as the first elements 102a, while
scattering elements that have been adjusted to a second state
having second electromagnetic properties are depicted as the second
elements 102b. The depiction of scattering elements having first
and second states corresponding to first and second electromagnetic
properties is not intended to be limiting: embodiments may provide
scattering elements that are discretely adjustable to select from a
discrete plurality of states corresponding to a discrete plurality
of different electromagnetic properties, or continuously adjustable
to select from a continuum of states corresponding to a continuum
of different electromagnetic properties. Moreover, the particular
pattern of adjustment that is depicted in FIG. 1 (i.e. the
alternating arrangement of elements 102a and 102b) is only an
exemplary configuration and is not intended to be limiting.
In the example of FIG. 1, the scattering elements 102a, 102b have
first and second couplings to the guided wave or surface wave 105
that are functions of the first and second electromagnetic
properties, respectively. For example, the first and second
couplings may be first and second polarizabilities of the
scattering elements at the frequency or frequency band of the
guided wave or surface wave. In one approach the first coupling is
a substantially nonzero coupling whereas the second coupling is a
substantially zero coupling. In another approach both couplings are
substantially nonzero but the first coupling is substantially
greater than (or less than) than the second coupling. On account of
the first and second couplings, the first and second scattering
elements 102a, 102b are responsive to the guided wave or surface
wave 105 to produce a plurality of scattered electromagnetic waves
having amplitudes that are functions of (e.g. are proportional to)
the respective first and second couplings. A superposition of the
scattered electromagnetic waves comprises an electromagnetic wave
that is depicted, in this example, as a plane wave 110 that
radiates from the surface scattering antenna 100.
The emergence of the plane wave may be understood by regarding the
particular pattern of adjustment of the scattering elements (e.g.
an alternating arrangement of the first and second scattering
elements in FIG. 1) as a pattern that defines a grating that
scatters the guided wave or surface wave 105 to produce the plane
wave 110. Because this pattern is adjustable, some embodiments of
the surface scattering antenna may provide adjustable gratings or,
more generally, holograms, where the pattern of adjustment of the
scattering elements may be selected according to principles of
holography. Suppose, for example, that the guided wave or surface
wave may be represented by a complex scalar input wave .PSI..sub.in
that is a function of position along the wave-propagating structure
104, and it is desired that the surface scattering antenna produce
an output wave that may be represented by another complex scalar
wave .PSI..sub.out. Then a pattern of adjustment of the scattering
elements may be selected that corresponds to an interference
pattern of the input and output waves along the wave-propagating
structure. For example, the scattering elements may be adjusted to
provide couplings to the guided wave or surface wave that are
functions of (e.g. are proportional to, or step-functions of) an
interference term given by Re[.PSI..sub.out.PSI.*.sub.in]. In this
way, embodiments of the surface scattering antenna may be adjusted
to provide arbitrary antenna radiation patterns by identifying an
output wave .PSI..sub.out corresponding to a selected beam pattern,
and then adjusting the scattering elements accordingly as above.
Embodiments of the surface scattering antenna may therefore be
adjusted to provide, for example, a selected beam direction (e.g.
beam steering), a selected beam width or shape (e.g. a fan or
pencil beam having a broad or narrow beamwidth), a selected
arrangement of nulls (e.g. null steering), a selected arrangement
of multiple beams, a selected polarization state (e.g. linear,
circular, or elliptical polarization), a selected overall phase, or
any combination thereof. Alternatively or additionally, embodiments
of the surface scattering antenna may be adjusted to provide a
selected near field radiation profile, e.g. to provide near-field
focusing and/or near-field nulls.
Because the spatial resolution of the interference pattern is
limited by the spatial resolution of the scattering elements, the
scattering elements may be arranged along the wave-propagating
structure with inter-element spacings that are much less than a
free-space wavelength corresponding to an operating frequency of
the device (for example, less than one-third, one-fourth, or
one-fifth of this free-space wavelength). In some approaches, the
operating frequency is a microwave frequency, selected from
frequency bands such as L, S, C, X, Ku, K, Ka, Q, U, V, E, W, F,
and D, corresponding to frequencies ranging from about 1 GHz to 170
GHz and free-space wavelengths ranging from millimeters to tens of
centimeters. In other approaches, the operating frequency is an RF
frequency, for example in the range of about 100 MHz to 1 GHz. In
yet other approaches, the operating frequency is a millimeter-wave
frequency, for example in the range of about 170 GHz to 300 GHz.
These ranges of length scales admit the fabrication of scattering
elements using conventional printed circuit board or lithographic
technologies.
In some approaches, the surface scattering antenna includes a
substantially one-dimensional wave-propagating structure 104 having
a substantially one-dimensional arrangement of scattering elements,
and the pattern of adjustment of this one-dimensional arrangement
may provide, for example, a selected antenna radiation profile as a
function of zenith angle (i.e. relative to a zenith direction that
is parallel to the one-dimensional wave-propagating structure). In
other approaches, the surface scattering antenna includes a
substantially two-dimensional wave-propagating structure 104 having
a substantially two-dimensional arrangement of scattering elements,
and the pattern of adjustment of this two-dimensional arrangement
may provide, for example, a selected antenna radiation profile as a
function of both zenith and azimuth angles (i.e. relative to a
zenith direction that is perpendicular to the two-dimensional
wave-propagating structure). Exemplary adjustment patterns and beam
patterns for a surface scattering antenna that includes a
two-dimensional array of scattering elements distributed on a
planar rectangular wave-propagating structure are depicted in FIGS.
2A-4B. In these exemplary embodiments, the planar rectangular
wave-propagating structure includes a monopole antenna feed that is
positioned at the geometric center of the structure. FIG. 2A
presents an adjustment pattern that corresponds to a narrow beam
having a selected zenith and azimuth as depicted by the beam
pattern diagram of FIG. 2B. FIG. 3A presents an adjustment pattern
that corresponds to a dual-beam far field pattern as depicted by
the beam pattern diagram of FIG. 3B. FIG. 4A presents an adjustment
pattern that provides near-field focusing as depicted by the field
intensity map of FIG. 4B (which depicts the field intensity along a
plane perpendicular to and bisecting the long dimension of the
rectangular wave-propagating structure).
In some approaches, the wave-propagating structure is a modular
wave-propagating structure and a plurality of modular
wave-propagating structures may be assembled to compose a modular
surface scattering antenna. For example, a plurality of
substantially one-dimensional wave-propagating structures may be
arranged, for example, in an interdigital fashion to produce an
effective two-dimensional arrangement of scattering elements. The
interdigital arrangement may comprise, for example, a series of
adjacent linear structures (i.e. a set of parallel straight lines)
or a series of adjacent curved structures (i.e. a set of
successively offset curves such as sinusoids) that substantially
fills a two-dimensional surface area. These interdigital
arrangements may include a feed connector having a tree structure,
e.g. a binary tree providing repeated forks that distribute energy
from the feed structure 108 to the plurality of linear structures
(or the reverse thereof). As another example, a plurality of
substantially two-dimensional wave-propagating structures (each of
which may itself comprise a series of one-dimensional structures,
as above) may be assembled to produce a larger aperture having a
larger number of scattering elements; and/or the plurality of
substantially two-dimensional wave-propagating structures may be
assembled as a three-dimensional structure (e.g. forming an A-frame
structure, a pyramidal structure, or other multi-faceted
structure). In these modular assemblies, each of the plurality of
modular wave-propagating structures may have its own feed
connector(s) 106, and/or the modular wave-propagating structures
may be configured to couple a guided wave or surface wave of a
first modular wave-propagating structure into a guided wave or
surface wave of a second modular wave-propagating structure by
virtue of a connection between the two structures.
In some applications of the modular approach, the number of modules
to be assembled may be selected to achieve an aperture size
providing a desired telecommunications data capacity and/or quality
of service, and/or a three-dimensional arrangement of the modules
may be selected to reduce potential scan loss. Thus, for example,
the modular assembly could comprise several modules mounted at
various locations/orientations flush to the surface of a vehicle
such as an aircraft, spacecraft, watercraft, ground vehicle, etc.
(the modules need not be contiguous). In these and other
approaches, the wave-propagating structure may have a substantially
non-linear or substantially non-planar shape whereby to conform to
a particular geometry, therefore providing a conformal surface
scattering antenna (conforming, for example, to the curved surface
of a vehicle).
More generally, a surface scattering antenna is a reconfigurable
antenna that may be reconfigured by selecting a pattern of
adjustment of the scattering elements so that a corresponding
scattering of the guided wave or surface wave produces a desired
output wave. Suppose, for example, that the surface scattering
antenna includes a plurality of scattering elements distributed at
positions {r.sub.j} along a wave-propagating structure 104 as in
FIG. 1 (or along multiple wave-propagating structures, for a
modular embodiment) and having a respective plurality of adjustable
couplings {.alpha..sub.j} to the guided wave or surface wave 105.
The guided wave or surface wave 105, as it propagates along or
within the (one or more) wave-propagating structure(s), presents a
wave amplitude A.sub.j and phase .phi..sub.j to the jth scattering
element; subsequently, an output wave is generated as a
superposition of waves scattered from the plurality of scattering
elements:
.function..theta..PHI..times..times..function..theta..PHI..times..alpha..-
times..times..times..times..phi..times..function..function..theta..PHI.
##EQU00001## where E(.theta.,.phi.) represents the electric field
component of the output wave on a far-field radiation sphere,
R.sub.j(.theta.,.phi.) represents a (normalized) electric field
pattern for the scattered wave that is generated by the jth
scattering element in response to an excitation caused by the
coupling .alpha..sub.j, and k(.theta.,.phi.) represents a wave
vector of magnitude .omega./c that is perpendicular to the
radiation sphere at (.theta.,.phi.). Thus, embodiments of the
surface scattering antenna may provide a reconfigurable antenna
that is adjustable to produce a desired output wave
E(.theta.,.phi.) by adjusting the plurality of couplings
{.alpha..sub.j} in accordance with equation (1).
The wave amplitude A.sub.j and phase .phi..sub.j of the guided wave
or surface wave are functions of the propagation characteristics of
the wave-propagating structure 104. Thus, for example, the
amplitude A.sub.j may decay exponentially with distance along the
wave-propagating structure, A.sub.j.about.A.sub.0
exp(-.kappa.x.sub.j), and the phase .phi..sub.j may advance
linearly with distance along the wave-propagating structure,
.phi..sub.j.about..phi..sub.0+.beta.x.sub.j, where .kappa. is a
decay constant for the wave-propagating structure, .beta. is a
propagation constant (wavenumber) for the wave-propagating
structure, and x.sub.j is a distance of the jth scattering element
along the wave-propagating structure. These propagation
characteristics may include, for example, an effective refractive
index and/or an effective wave impedance, and these effective
electromagnetic properties may be at least partially determined by
the arrangement and adjustment of the scattering elements along the
wave-propagating structure. In other words, the wave-propagating
structure, in combination with the adjustable scattering elements,
may provide an adjustable effective medium for propagation of the
guided wave or surface wave, e.g. as described in D. R. Smith et
al, previously cited. Therefore, although the wave amplitude
A.sub.j and phase .phi..sub.j of the guided wave or surface wave
may depend upon the adjustable scattering element couplings
{.alpha..sub.j} (i.e. A.sub.i=A.sub.j({.alpha..sub.j}),
.phi..sub.i=.phi..sub.i({.alpha..sub.j})), in some embodiments
these dependencies may be substantially predicted according to an
effective medium description of the wave-propagating structure.
In some approaches, the reconfigurable antenna is adjustable to
provide a desired polarization state of the output wave
E(.theta.,.phi.). Suppose, for example, that first and second
subsets LP.sup.(1) and LP.sup.(2) of the scattering elements
provide (normalized) electric field patterns
R.sup.(1)(.theta.,.phi.) and R.sup.(2)(.theta.,.phi.),
respectively, that are substantially linearly polarized and
substantially orthogonal (for example, the first and second
subjects may be scattering elements that are perpendicularly
oriented on a surface of the wave-propagating structure 104). Then
the antenna output wave E(.theta.,.phi.) may be expressed as a sum
of two linearly polarized components:
E(.theta.,.phi.)=E.sup.(1)(.theta.,.phi.)+E.sup.(2)(.theta.,.phi.)=.LAMBD-
A..sup.(1)R.sup.(1)(.theta.,.phi.)+.LAMBDA..sup.(2)R.sup.(2)(.theta.,.phi.-
), (2) where
.LAMBDA..times..function..theta..PHI..di-elect
cons..times..times..alpha..times..times..times..times..phi..times..functi-
on..function..theta..PHI. ##EQU00002## are the complex amplitudes
of the two linearly polarized components. Accordingly, the
polarization of the output wave E(.theta.,.phi.) may be controlled
by adjusting the plurality of couplings {.alpha..sub.j} in
accordance with equations (2)-(3), e.g. to provide an output wave
with any desired polarization (e.g. linear, circular, or
elliptical).
Alternatively or additionally, for embodiments in which the
wave-propagating structure has a plurality of feeds (e.g. one feed
for each "finger" of an interdigital arrangement of one-dimensional
wave-propagating structures, as discussed above), a desired output
wave E(.theta.,.phi.) may be controlled by adjusting gains of
individual amplifiers for the plurality of feeds. Adjusting a gain
for a particular feed line would correspond to multiplying the
A.sub.j's by a gain factor G for those elements j that are fed by
the particular feed line. Especially, for approaches in which a
first wave-propagating structure having a first feed (or a first
set of such structures/feeds) is coupled to elements that are
selected from LP.sup.(1) and a second wave-propagating structure
having a second feed (or a second set of such structures/feeds) is
coupled to elements that are selected from LP.sup.(2),
depolarization loss (e.g., as a beam is scanned off-broadside) may
be compensated by adjusting the relative gain(s) between the first
feed(s) and the second feed(s).
Turning now to a consideration of modulation patterns for surface
scattering antennas: recall, as discussed above, that the guided
wave or surface wave may be represented by a complex scalar input
wave .PSI..sub.in that is a function of position along the
wave-propagating structure. To produce an output wave that may be
represented by another complex scalar wave .PSI..sub.out, a pattern
of adjustments of the scattering elements may be selected that
corresponds to an interference pattern of the input and output
waves along the wave-propagating structure. For example, the
scattering elements may be adjusted to provide couplings to the
guided wave or surface wave that are functions of a complex
continuous hologram function h=.PSI..sub.out.PSI.*.sub.in.
In some approaches, the scattering elements can be adjusted only to
approximate the ideal complex continuous hologram function
h=.PSI..sub.out.PSI.*.sub.in. For example, because the scattering
elements are positioned at discrete locations along the
wave-propagating structure, the hologram function must be
discretized. Furthermore, in some approaches, the set of possible
couplings between a particular scattering elements and the
waveguide is a restricted set of couplings; for example, an
embodiment may provide only a finite set of possible couplings
(e.g. a "binary" or "on-off" scenario in which there are only two
available couplings for each scattering element, or a "grayscale"
scenario in which there are N available couplings for each
scattering element); and/or the relationship between the amplitude
and phase of each coupling may be constrained (e.g. by a
Lorentzian-type resonance response function). Thus, in some
approaches, the ideal complex continuous hologram function is
approximated by an actual modulation function defined on a
discrete-valued domain (for the discrete positions of the
scattering elements) and having a discrete-valued range (for the
discrete available tunable settings of the scattering
elements).
Consider, for example, a one-dimensional surface scattering antenna
on which it is desired to impose an ideal hologram function defined
as a simple sinusoid corresponding to a single wavevector (the
following disclosure, relating to the one-dimensional sinusoid, is
not intended to be limiting and the approaches set forth are
applicable to other two-dimensional hologram patterns). Various
discrete modulation functions may be used to approximate this ideal
hologram function. In a "binary" scenario where only two values of
individual scattering element coupling are available, one approach
is to apply a Heaviside function to the sinusoid, creating a simple
square wave. Regardless of the density of scattering elements, that
Heaviside function will have approximately half the cells on and
half off, in a steady repeating pattern. Unlike the spectrally pure
sinusoid though, a square wave contains an (infinite) series of
higher harmonics. In these approaches, the antenna may be designed
so that the higher harmonics correspond to evanescent waves, making
them non-radiating, but their aliases do still map into
non-evanescent waves and radiate as grating lobes.
An illustrative example of the discretization and aliasing effect
is shown in FIGS. 5A-5F. FIG. 5A depicts a continuous hologram
function that is a simple sinusoid 500; in Fourier space, this is
represented as a single Fourier mode 510 as shown in FIG. 5D. When
the Heaviside function is applied to the sinusoid, the result is a
square wave 502 as shown in FIG. 5B; in Fourier space, the square
wave includes the fundamental Fourier mode 510 and an (infinite)
series of higher harmonics 511, 512, 513, etc. as shown in FIG. 5E.
Finally, when the square wave is sampled at a discrete set of
locations corresponding to the discrete locations of the scattering
elements, the result is a discrete-valued function 504 on a
discrete domain, as shown in FIG. 5C (here assuming a lattice
constant a).
The sampling of the square wave at a discrete set of locations
leads to an aliasing effect in Fourier space, as shown in FIG. 5F.
In this illustration, the sampling with a lattice constant a leads
to a "folding" of the Fourier spectrum around the Nyquist spatial
frequency .pi./a, creating aliases 522 and 523 for the original
harmonics 512 and 513, respectively. Supposing that the aperture
has an evanescent cutoff given by 2.pi.f/c as shown (where f is an
operating frequency of the antenna and c is the speed of light in
an ambient medium surrounding the antenna, which can be vacuum,
air, a dielectric material, etc.), one of the harmonics (513) is
aliased into the non-evanescent spatial frequency range (523) and
can radiate as a grating lobe. Note that in this example, the first
harmonic 511 is unaliased but also within the non-evanescent
spatial frequency range, so it can generate another undesirable
side lobe
The Heaviside function is not the only choice for a binary
hologram, and other choices may eliminate, average, or otherwise
mitigate the higher harmonics and the resulting side/grating lobes.
A useful way to view these approaches is as attempting to "smooth"
or "blur" the sharp corners in the Heaviside without resorting to
values other than 0 and 1. For example, the single step of the
Heaviside function may be replaced by a function that resembles a
pulse-width-modulated (PWM) square wave with a duty cycle that
gradually increases from 0 to 1 over the range of the sinusoid.
Alternatively, a probabilistic or dithering approach may be used to
determine the settings of the individual scattering elements, for
example by randomly adjusting each scattering element to the "on"
or "off" state according to a probability that gradually increases
from 0 to 1 over the range of the sinusoid.
In some approaches, the binary approximation of the hologram may be
improved by increasing the density of scattering elements. An
increased density results in a larger number of adjustable
parameters that can be optimized, and a denser array results in
better homogenization of electromagnetic parameters.
Alternatively or additionally, in some approaches the binary
approximation of the hologram may be improved by arranging the
elements in a non-uniform spatial pattern. If the scattering
elements are placed on non-uniform grid, the rigid periodicity of
the Heaviside modulation is broken, which spreads out the higher
harmonics. The non-uniform spatial pattern can be a random
distribution, e.g. with a selected standard deviation and mean,
and/or it can be a gradient distribution, with a density of
scattering elements that varies with position along the
wave-propagating structure. For example, the density may be larger
near the center of the aperture to realize an amplitude
envelope.
Alternatively or additionally, in some approaches the binary
approximation of the hologram may be improved by arranging the
scattering elements to have non-uniform nearest neighbor couplings.
Jittering these nearest-neighbor couplings can blur the
k-harmonics, yielding reduced side/grating lobes. For example, in
approaches that use a via fence to reduce coupling or crosstalk
between adjacent unit cells, the geometry of the via fence (e.g.
the spacing between vias, the sizes of the via holes, or the
overall length of the fence) can be varied cell-by-cell. In other
approaches that use a via fence to separate the cavities for a
series of scattering elements that are cavity-fed slots, again the
geometry of the via fence can be varied cell-by-cell. This
variation can correspond to a random distribution, e.g. with a
selected standard deviation and mean, and/or it can be a gradient
distribution, with a nearest-neighbor coupling that varies with
position along the wave-propagating structure. For example, the
nearest-neighbor coupling may be largest (or smallest) near the
center of the aperture.
Alternatively or additionally, in some approaches the binary
approximation of the hologram may be improved by increasing the
nearest-neighbor couplings between the scattering elements. For
example, small parasitic elements can be introduced to act as
"blurring pads" between the unit cells. The pad can be designed to
have a smaller effect between two cells that are both "on" or both
"off," and a larger effect between an "on" cell and an "off" cell,
e.g. by radiating with an average of the two adjacent cells to
realize a mid-point modulation amplitude.
Alternatively or additionally, in some approaches the binary
approximation of the hologram may be improved using error
propagation or error diffusion techniques to determine the
modulation pattern. An error propagation technique may involve
considering the desired value of a pure sinusoid modulation and
tracking a cumulative difference between that and the Heaviside (or
other discretization function). The error accumulates, and when it
reaches a threshold it carries over to the current cell. For a
two-dimensional scattering antenna composed of a set of rows, the
error propagation may be performed independently on each row; or
the error propagation may be performed row-by-row by carrying over
an error tally from the end of row to the beginning of the next
row; or the error propagation may be performed multiple times along
different directions (e.g. first along the rows and then
perpendicular to the rows); or the error propagation may use a
two-dimensional error propagation kernel as with Floyd-Steinberg or
Jarvis-Judice-Ninke error diffusion. For an embodiment using a
plurality of one-dimensional waveguides to compose a
two-dimensional aperture, the rows for error diffusion can
correspond to individual one-dimensional waveguides, or the rows
for error diffusion can be oriented perpendicularly to the
one-dimensional waveguides. In other approaches, the rows can be
defined with respect to the waveguide mode, e.g. by defining the
rows as a series of successive phase fronts of the waveguide mode
(thus, a center-fed parallel plate waveguide would have "rows" that
are concentric circles around the feed point). In yet other
approaches, the rows can be selected depending on the hologram
function that is being discretized--for example, the rows can be
selected as a series of contours of the hologram function, so that
the error diffusion proceeds along directions of small variation of
the hologram function.
Alternatively or additionally, in some approaches grating lobes can
be reduced by using scattering elements with increased directivity.
Often the grating lobes appear far from the main beam; if the
individual scattering elements are designed to have increased
broadside directivity, large-angle aliased grating lobes may be
significantly reduced in amplitude.
Alternatively or additionally, in some approaches grating lobes can
be reduced by changing the input wave .PSI..sub.in along the
wave-propagating structure. By changing the input wave throughout a
device, the spectral harmonics are varied, and large grating lobes
may be avoided. For example, for a two-dimensional scattering
antenna composed of a set of parallel one-dimensional rows, the
input wave can be changed by alternating feeding directions for
successive rows, or by alternating feeding directions for the top
and bottom halves of the antenna. As another example, the effective
index of propagation along the wave-propagating structure can be
varied with position along the wave-propagating structure, by
varying some aspect of the wave-propagating structure geometry
(e.g. the positions of the vias in a substrate-integrated
waveguide), by varying dielectric value (e.g. the filling fraction
of a dielectric in a closed waveguide), by actively loading the
wave-propagating structure, etc.
Alternatively or additionally, in some approaches the grating lobes
can be reduced by introducing structure on top of the surface
scattering antenna. For example, a fast-wave structure (such as a
dispersive plasmonic or surface wave structure or an air-core-based
waveguide structure) placed on top of the the surface-scattering
antenna can be designed to propagate the evanescent grating lobe
and carry it out to a load dump before it aliases into the
non-evanescent region. As another example, a directivity-enhancing
structure (such as an array of collimating GRIN lenses) can be
placed on top of the surface scattering antenna to enhance the
individual directivities of the scattering elements.
While some approaches, as discussed above, arrange the scattering
elements in a non-uniform spatial pattern, other approaches
maintain a uniform arrangement of the scattering elements but vary
their "virtual" locations to be used in calculating the modulation
pattern. Thus the scattering elements can physically still exist on
a uniform grid (or any other fixed physical pattern), but their
virtual location is shifted in the computation algorithm. For
example, the virtual locations can be determined by applying a
random displacement to the physical locations, the random
displacement having a zero mean and controllable distribution,
analogous to classical dithering. Alternatively, the virtual
locations can be calculated by adding a non-random displacement
from the physical locations, the displacement varying with position
along the wave-propagating structure (e.g. with intentional
gradients over various length scales).
In some approaches, undesirable grating lobes can be reduced by
flipping individual bits corresponding to individual scattering
elements. In these approaches, each element can be described as a
single bit which contributes spectrally to both the desired
fundamental modulation and to the higher harmonics that give rise
to grating lobes. Thus, single bits that contribute to harmonics
more than the fundamental can be flipped, reducing the total
harmonics level while leaving the fundamental relatively
unaffected.
Alternatively or additionally, undesirable grating lobes can be
reduced by applying a spectrum (in k-space) of modulation
fundamentals rather than a single fundamental, i.e. range of
modulation wavevectors, to disperse energy put into higher
harmonics. This is a form of modulation dithering. Because higher
harmonics pick up an additional a wave-vector phase when they alias
back into the visible, grating lobes resulting from different
modulation wavevectors can be spread in radiative angle even while
the main beams overlap. This spectrum of modulation wavevectors can
be flat, Gaussian, or any other distribution across a modulation
wavevector bandwidth.
Alternatively or additionally, undesirable grating lobes can be
reduced by "chopping" the range-discretized hologram (e.g. after
applying the Heaviside function but before sampling at the discrete
set of scattering element locations) to selectively reduce or
eliminate higher harmonics. Selective elimination of square wave
harmonics is described, for example, in H. S. Patel and R. G. Hoft,
"Generalized Techniques of Harmonic Elimination and Voltage Control
in Thyristor Inverters: Part I--Harmonic Elimination," IEEE Trans.
Ind. App. Vol. IA-9, 310 (1973), herein incorporated by reference.
For example, the square wave 502 of FIG. 5B can be modified with
"chops" that eliminate the harmonics 511 and 513 (as shown in FIG.
5E) so that neither the harmonic 511 nor the aliased harmonic 531
(as shown in FIG. 5F) will generate grating lobes.
Alternatively or additionally, undesirable grating lobes may be
reduced by adjusting the wavevector of the modulation pattern.
Adjusting the wavevector of the modulation pattern shifts the
primary beam, but shifts grating lobes coming from aliased beams to
a greater degree (due to the additional a phase shift on every
alias). Adjustment of the phase and wavevector of the applied
modulation pattern can be used to intentionally form constructive
and destructive interference of the grating lobes, side lobes, and
main beam. Thus, allowing very minor changes in the angle and phase
of the main radiated beam can grant a large parameter space in
which to optimize/minimize grating lobes.
Alternatively or additionally, the antenna modulation pattern can
be selected according to an optimization algorithm that optimizes a
particular cost function. For example, the modulation pattern may
be calculated to optimize: realized gain (maximum total intensity
in the main beam); relative minimization of the highest side lobe
or grating lobe relative to main beam; minimization of main-beam
FWHM (beam width); or maximization of main-beam directivity (height
above all integrated side lobes and grating lobes); or any
combination thereof (e.g. by using a collective cost function that
is a weighted sum of individual cost functions, or by selecting a
Pareto optimum of individual cost functions). The optimization can
be either global (searching the entire space of antenna
configurations to optimize the cost function) or local (starting
from an initial guess and applying an optimization algorithm to
find a local extremum of the cost function).
Various optimization algorithms may be utilized to perform the
optimization of the desired cost function. For example, the
optimization may proceed using discrete optimization variables
corresponding to the discrete adjustment states of the scattering
elements, or the optimization may proceed using continuous
optimization variables that can be mapped to the discrete
adjustment states by a smoothed step function (e.g. a smoothed
Heaviside function for a binary antenna or a smoothed sequential
stair-step function for a grayscale antenna). Other optimization
approaches can include optimization with a genetic optimization
algorithm or a simulated annealing optimization algorithm.
The optimization algorithm can involve an iterative process that
includes identifying a trial antenna configuration, calculating a
gradient of the cost function for the antenna configuration, and
then selecting a subsequent trial configuration, repeating the
process until some termination condition is met. The gradient can
be calculated by, for example, calculating finite-difference
estimates of the partial derivatives of the cost function with
respect to the individual optimization variables. For N scattering
elements, this might involve performing N full-wave simulations, or
performing N measurements of a test antenna in a test environment
(e.g. an anechoic chamber). Alternatively, the gradient may be
calculable by an adjoint sensitivity method that entails solving a
single adjoint problem instead of N finite-difference problems;
adjoint sensitivity models are available in conventional numerical
software packages such as HFSS or CST Microwave Studio. Once the
gradient is obtained, a subsequent trial configuration can be
calculated using various optimization iteration approaches such as
quasi-Newton methods or conjugate gradient methods. The iterative
process may terminate, for example, when the norm of the cost
function gradient becomes sufficiently small, or when the cost
function reaches a satisfactory minimum (or maximum).
In some approaches, the optimization can be performed on a reduced
set of modulation patterns. For example, for a binary (grayscale)
antenna with N scattering elements, there are 2.sup.N (or g.sup.N,
for g grayscale levels) possible modulation patterns, but the
optimization may be constrained to consider only those modulation
patterns that yield a desired primary spectral content in the
output wave .PSI..sub.out, and/or the optimization may be
constrained to consider only those modulation patterns which have a
spatial on-off fraction within a known range relevant for the
design.
While the above discussion of modulation patterns has focused on
binary embodiments of the surface scattering antenna, it will be
appreciated that all of the various approaches described above are
directly applicable to grayscale approaches where the individual
scattering elements are adjustable between more than two
configurations.
With reference now to FIG. 6, an illustrative embodiment is
depicted as a system block diagram. The system includes a surface
scattering antenna 600 coupled to control circuitry 610 operable to
adjust the surface scattering to any particular antenna
configuration. The system optionally includes a storage medium 620
on which is written a set of pre-calculated antenna configurations.
For example, the storage medium may include a look-up table of
antenna configurations indexed by some relevant operational
parameter of the antenna, such as beam direction, each stored
antenna configuration being previously calculated according to one
or more of the approaches described above. Then, the control
circuitry 610 would be operable to read an antenna configuration
from the storage medium and adjust the antenna to the selected,
previously-calculated antenna configuration. Alternatively, the
control circuitry 610 may include circuitry operable to calculate
an antenna configuration according to one or more of the approaches
described above, and then to adjust the antenna for the
presently-calculated antenna configuration.
The foregoing detailed description has set forth various
embodiments of the devices and/or processes via the use of block
diagrams, flowcharts, and/or examples. Insofar as such block
diagrams, flowcharts, and/or examples contain one or more functions
and/or operations, it will be understood by those within the art
that each function and/or operation within such block diagrams,
flowcharts, or examples can be implemented, individually and/or
collectively, by a wide range of hardware, software, firmware, or
virtually any combination thereof. In one embodiment, several
portions of the subject matter described herein may be implemented
via Application Specific Integrated Circuits (ASICs), Field
Programmable Gate Arrays (FPGAs), digital signal processors (DSPs),
or other integrated formats. However, those skilled in the art will
recognize that some aspects of the embodiments disclosed herein, in
whole or in part, can be equivalently implemented in integrated
circuits, as one or more computer programs running on one or more
computers (e.g., as one or more programs running on one or more
computer systems), as one or more programs running on one or more
processors (e.g., as one or more programs running on one or more
microprocessors), as firmware, or as virtually any combination
thereof, and that designing the circuitry and/or writing the code
for the software and or firmware would be well within the skill of
one of skill in the art in light of this disclosure. In addition,
those skilled in the art will appreciate that the mechanisms of the
subject matter described herein are capable of being distributed as
a program product in a variety of forms, and that an illustrative
embodiment of the subject matter described herein applies
regardless of the particular type of signal bearing medium used to
actually carry out the distribution. Examples of a signal bearing
medium include, but are not limited to, the following: a recordable
type medium such as a floppy disk, a hard disk drive, a Compact
Disc (CD), a Digital Video Disk (DVD), a digital tape, a computer
memory, etc.; and a transmission type medium such as a digital
and/or an analog communication medium (e.g., a fiber optic cable, a
waveguide, a wired communications link, a wireless communication
link, etc.).
In a general sense, those skilled in the art will recognize that
the various aspects described herein which can be implemented,
individually and/or collectively, by a wide range of hardware,
software, firmware, or any combination thereof can be viewed as
being composed of various types of "electrical circuitry."
Consequently, as used herein "electrical circuitry" includes, but
is not limited to, electrical circuitry having at least one
discrete electrical circuit, electrical circuitry having at least
one integrated circuit, electrical circuitry having at least one
application specific integrated circuit, electrical circuitry
forming a general purpose computing device configured by a computer
program (e.g., a general purpose computer configured by a computer
program which at least partially carries out processes and/or
devices described herein, or a microprocessor configured by a
computer program which at least partially carries out processes
and/or devices described herein), electrical circuitry forming a
memory device (e.g., forms of random access memory), and/or
electrical circuitry forming a communications device (e.g., a
modem, communications switch, or optical-electrical equipment).
Those having skill in the art will recognize that the subject
matter described herein may be implemented in an analog or digital
fashion or some combination thereof.
All of the above U.S. patents, U.S. patent application
publications, U.S. patent applications, foreign patents, foreign
patent applications and non-patent publications referred to in this
specification and/or listed in any Application Data Sheet, are
incorporated herein by reference, to the extent not inconsistent
herewith.
One skilled in the art will recognize that the herein described
components (e.g., steps), devices, and objects and the discussion
accompanying them are used as examples for the sake of conceptual
clarity and that various configuration modifications are within the
skill of those in the art. Consequently, as used herein, the
specific exemplars set forth and the accompanying discussion are
intended to be representative of their more general classes. In
general, use of any specific exemplar herein is also intended to be
representative of its class, and the non-inclusion of such specific
components (e.g., steps), devices, and objects herein should not be
taken as indicating that limitation is desired.
With respect to the use of substantially any plural and/or singular
terms herein, those having skill in the art can translate from the
plural to the singular and/or from the singular to the plural as is
appropriate to the context and/or application. The various
singular/plural permutations are not expressly set forth herein for
sake of clarity.
While particular aspects of the present subject matter described
herein have been shown and described, it will be apparent to those
skilled in the art that, based upon the teachings herein, changes
and modifications may be made without departing from the subject
matter described herein and its broader aspects and, therefore, the
appended claims are to encompass within their scope all such
changes and modifications as are within the true spirit and scope
of the subject matter described herein. Furthermore, it is to be
understood that the invention is defined by the appended claims. It
will be understood by those within the art that, in general, terms
used herein, and especially in the appended claims (e.g., bodies of
the appended claims) are generally intended as "open" terms (e.g.,
the term "including" should be interpreted as "including but not
limited to," the term "having" should be interpreted as "having at
least," the term "includes" should be interpreted as "includes but
is not limited to," etc.). It will be further understood by those
within the art that if a specific number of an introduced claim
recitation is intended, such an intent will be explicitly recited
in the claim, and in the absence of such recitation no such intent
is present. For example, as an aid to understanding, the following
appended claims may contain usage of the introductory phrases "at
least one" and "one or more" to introduce claim recitations.
However, the use of such phrases should not be construed to imply
that the introduction of a claim recitation by the indefinite
articles "a" or "an" limits any particular claim containing such
introduced claim recitation to inventions containing only one such
recitation, even when the same claim includes the introductory
phrases "one or more" or "at least one" and indefinite articles
such as "a" or "an" (e.g., "a" and/or "an" should typically be
interpreted to mean "at least one" or "one or more"); the same
holds true for the use of definite articles used to introduce claim
recitations. In addition, even if a specific number of an
introduced claim recitation is explicitly recited, those skilled in
the art will recognize that such recitation should typically be
interpreted to mean at least the recited number (e.g., the bare
recitation of "two recitations," without other modifiers, typically
means at least two recitations, or two or more recitations).
Furthermore, in those instances where a convention analogous to "at
least one of A, B, and C, etc." is used, in general such a
construction is intended in the sense one having skill in the art
would understand the convention (e.g., "a system having at least
one of A, B, and C" would include but not be limited to systems
that have A alone, B alone, C alone, A and B together, A and C
together, B and C together, and/or A, B, and C together, etc.). In
those instances where a convention analogous to "at least one of A,
B, or C, etc." is used, in general such a construction is intended
in the sense one having skill in the art would understand the
convention (e.g., "a system having at least one of A, B, or C"
would include but not be limited to systems that have A alone, B
alone, C alone, A and B together, A and C together, B and C
together, and/or A, B, and C together, etc.). It will be further
understood by those within the art that virtually any disjunctive
word and/or phrase presenting two or more alternative terms,
whether in the description, claims, or drawings, should be
understood to contemplate the possibilities of including one of the
terms, either of the terms, or both terms. For example, the phrase
"A or B" will be understood to include the possibilities of "A" or
"B" or "A and B."
With respect to the appended claims, those skilled in the art will
appreciate that recited operations therein may generally be
performed in any order. Examples of such alternate orderings may
include overlapping, interleaved, interrupted, reordered,
incremental, preparatory, supplemental, simultaneous, reverse, or
other variant orderings, unless context dictates otherwise. With
respect to context, even terms like "responsive to," "related to,"
or other past-tense adjectives are generally not intended to
exclude such variants, unless context dictates otherwise.
While various aspects and embodiments have been disclosed herein,
other aspects and embodiments will be apparent to those skilled in
the art. The various aspects and embodiments disclosed herein are
for purposes of illustration and are not intended to be limiting,
with the true scope and spirit being indicated by the following
claims.
* * * * *
References